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On Some Models for Value-At-Risk

Author

Listed:
  • Philip Yu
  • Wai Keung Li
  • Shusong Jin

Abstract

The idea of statistical learning can be applied in financial risk management. In recent years, value-at-risk (VaR) has become the standard tool for market risk measurement and management. For better VaR estimation, Engle and Manganelli (2004) introduced the conditional autoregressive value-at-risk (CAViaR) model to estimate the VaR directly by quantile regression. To entertain the nonlinearity and structural change in the VaR, we extend the CAViaR idea using two approaches: the threshold GARCH (TGARCH) and the mixture-GARCH models. The estimation method of these models are proposed. Our models should possess all the advantages of the CAViaR model and enhance the nonlinear structure. The methods are applied to the S&P500, Hang Seng, Nikkei and Nasdaq indices to illustrate our models.

Suggested Citation

  • Philip Yu & Wai Keung Li & Shusong Jin, 2010. "On Some Models for Value-At-Risk," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 622-641.
    • Handle: RePEc:taf:emetrv:v:29:y:2010:i:5-6:p:622-641
    DOI: 10.1080/07474938.2010.481972
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    References listed on IDEAS

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    1. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    2. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
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    Citations

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    Cited by:

    1. Yuzhi Cai & Julian Stander, 2020. "The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 395-424.
    2. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    3. Peng, Wei, 2021. "The transmission of default risk between banks and countries based on CAViaR models," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 500-509.
    4. Peng, Wei & Hu, Shichao & Chen, Wang & Zeng, Yu-feng & Yang, Lu, 2019. "Modeling the joint dynamic value at risk of the volatility index, oil price, and exchange rate," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 137-149.
    5. Huang, Jiefei & Xu, Yang & Song, Yuping, 2022. "A high-frequency approach to VaR measures and forecasts based on the HAR-QREG model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    6. Yuzhi Cai & Thanaset Chevapatrakul & Danilo V. Mascia, 2021. "How is price explosivity triggered in the cryptocurrency markets?," Annals of Operations Research, Springer, vol. 307(1), pages 37-51, December.
    7. Ahmed Ali & Granberg Mark & Uddin Gazi Salah & Troster Victor, 2022. "Asymmetric dynamics between uncertainty and unemployment flows in the United States," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(1), pages 155-172, February.
    8. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    9. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    10. Yuzhi Cai, 2021. "Estimating expected shortfall using a quantile function model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4332-4360, July.
    11. Mateusz Buczyński & Marcin Chlebus, 2019. "Old-fashioned parametric models are still the best. A comparison of Value-at-Risk approaches in several volatility states," Working Papers 2019-12, Faculty of Economic Sciences, University of Warsaw.
    12. Abad, Pilar & Benito, Sonia, 2013. "A detailed comparison of value at risk estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 258-276.
    13. Laura Garcia-Jorcano & Alfonso Novales, 2020. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 35(3), pages 1411-1448, September.
    14. Jian, Zhihong & Lu, Haisong & Zhu, Zhican & Xu, Huiling, 2023. "Frequency heterogeneity of tail connectedness: Evidence from global stock markets," Economic Modelling, Elsevier, vol. 125(C).
    15. Yuzhi Cai & Guodong Li, 2018. "A novel approach to modelling the distribution of financial returns," Working Papers 2018-22, Swansea University, School of Management.
    16. Yun-Shi Dai & Peng-Fei Dai & Wei-Xing Zhou, 2023. "Tail dependence structure and extreme risk spillover effects between the international agricultural futures and spot markets," Papers 2303.11030, arXiv.org.

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